We begin by exercising the model to determine whether our theory accurately predicts changes in brain state induced by direct electrical stimulation. Specifically, we simulate Eq. REF  to predict how stimulation alone (independent of other ongoing intrinsic dynamics) will alter brain state, given the structural adjacency matrix \(\mathbf {A}\)  and the initial state \(x(0)\)  comprised of the ECoG power at every node recorded pre-stimulation (\(x_{i} = 1\)  if node \(i\)  is a region without electrodes, and the \(z\) -scored power otherwise; see Supplement for further details). For each stimulation event, we calculate the Pearson's correlation coefficient between the empirically observed post-stimulation state (an electrode by frequency matrix) and the predicted post-stimulation state at every time point in the simulated trajectory \(x(t)\) . To measure the capacity of the model simulation to predict the post-stimulation state, we measure the signed maximum correlation achieved across the model simulation time of arbitrary units. Accordingly, we compute a maximum correlation value between the model prediction and the empirically observed post-stimulation state for each stimulation trial (\(\mu \)  = 0.036 \(\pm \)  0.019; Fig. REF A) and we observe that the mean of the maximum correlation values is significantly greater than zero (\(t\) -test \(N = 16\) , \(t = 5.83\) , \(p = 3.31 \times 10^{-5}\) ). We note that this correlation represents the impact of stimulation alone on linear dynamics, and does not take into account any other incoming stimuli from the surrounding environment, any ongoing cognitive or metabolic processes, nonlinear dependencies, or inter-frequency interactions [1]}, [2]}, [3]}. Complementing this estimate, we were also interested in the time point (measured in arbitrary units) at which the trial reached its largest magnitude correlation (positive or negative) before decaying towards zero. We observed that the time at which the peak magnitude occurred differed across trials, having a mean of \(298 \pm 114\)  (Fig. REF B).
<FIGURE><FIGURE>